1. Field of the Invention
This invention relates to the dynamics of time-limiting and frequency-limiting properties in the hearing mechanism auditory perception, and in particular to a Hilbert space model of at least auditory perception, and further as to systems and methods of at least signal processing, signal encoding, user/machine interfaces, data sonification, and human language design.
2. Background of the Invention
Most of the attempts to explain attributes of auditory perception are focused on the perception of steady-state phenomenon. These tend to separate affairs in time and frequency domains and ignore their interrelationships. A function cannot be both time and frequency-limited, and there are trade-offs between these limitations.
The temporal and pitch perception aspects of human hearing comprise a frequency-limiting property or behavior in the frequency range between approximately 20 Hz and 20 KHz. The range slightly varies for each individual's biological and environmental factors, but human ears are not able to detect vibrations or sound with lesser or greater frequency than in roughly this range. The temporal and pitch perception aspects of human hearing also comprise a time-limited property or behavior in that human hearing perceives and analyzes stimuli within a time correlation window of 50 msec (sometimes called the “time constant” of human hearing). A periodic audio stimulus with period of vibration faster than 50 msec is perceived in hearing as a tone or pitch, while a periodic audio stimulus with period of vibration slower than 50 msec will either not be perceived in hearing or will be perceived in hearing as a periodic sequence of separate discrete events. The ˜50 msec time correlation window and the ˜20 Hz lower frequency limit suggest a close interrelationship in that the period of a 20 Hz periodic waveform is in fact 50 msec.
As will be shown, these can be combined to create a previously unknown Hilbert-space of eigenfunctions modeling auditory perception. This new Hilbert-space model can be used to study aspects of the signal processing structure of human hearing. Further, the resulting eigenfunctions themselves may be used to create a wide range of novel systems and methods signal processing, signal encoding, user/machine interfaces, data sonification, and human language design.
Additionally, the ˜50 msec time correlation window and the ˜20 Hz lower frequency limit appear to be a property of the human brain and nervous system that may be shared with other senses. As a result, the Hilbert-space of eigenfunctions may be useful in modeling aspects of other senses, for example, visual perception of image sequences and motion in visual image scenes.
For example, there is a similar ˜50 msec time correlation window and the ˜20 Hz lower frequency limit property in the visual system. Sequences of images, as in a flipbook, cinema, or video, start blending into perceived continuous image or motion as the frame rate of images passes a threshold rate of about 20 frames per second. At 20 frames per second, each image is displayed for 50 msec. At a slower rate, the individual images are seen separately in a sequence while at a faster rate the perception of continuous motion improves and quickly stabilizes. Similarly, objects in a visual scene visually oscillating in some attribute (location, color, texture, etc.) at rates somewhat less than ˜20 Hz can be followed by human vision, but at oscillation rates approaching ˜20 Hz and above human vision perceives these as a blur.